Question 64

The line passing through (-2,5) and (6,b) is perpendicular to the line 20x + 5y = 3. Find b?

Solution

Slope of line having equation : $$ax + by + c = 0$$ is $$\frac{-a}{b}$$

=> Slope of line $$20x + 5y = 3$$ is $$\frac{-20}{5} = -4$$

Slope line passing through (-2,5) and (6,b) = $$\frac{b - 5}{6 + 2} = \frac{(b - 5)}{8}$$

Also, product of slopes of two perpendicular lines is -1

=> $$\frac{(b - 5)}{8} \times -4 = -1$$

=> $$b - 5 = \frac{8}{4} = 2$$

=> $$b = 2 + 5 = 7$$

=> Ans - (C)

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